Sunday, December 7, 2014

Fossil fuels: are we on the edge of the Seneca cliff?

"It would be some consolation for
the feebleness of our selves and our works if all things should perish
as slowly as they come into being; but as it is, increases are of
sluggish growth, but the way to ruin is rapid." Lucius Anneaus Seneca,
Letters to Lucilius, n. 91.

This observation by Seneca seems to be valid for many modern cases, including the production of a nonrenewable resource such as crude oil. Are we on the edge of the "Seneca cliff?"

It is a well known tenet of people working in system dynamics that there exist plenty of cases of solutions worsening the problem. Often, people appear to be perfectly able to understand what the problem is, but, just as often, they tend to act on it in the wrong way. It is a concept also expressed as "pushing the lever in the wrong direction."

With fossil fuels, we all understand that we have a depletion problem, but the solution, so far, has been to drill more, to drill deeper, and to keep drilling. Squeezing out some fuel by all possible sources, no matter how difficult and expensive, could offset the decline of conventional fields and keep production growing for the past few years. But is it a real solution? That is, won't we pay the present growth with a faster decline in the future?

This question can be described in terms of the "Seneca Cliff", a concept that I proposed a few years ago to describe how the production of a non renewable resource may show a rapid decline after passing its production peak. A behavior that can be shown graphically as follows:

It is not just a theoretical model: there are several historical cases where the production of a resource collapsed after having reached a peak. For instance, here are the data for the Caspian sturgeon, a case that I termed "peak caviar".

Do we risk to see something like this in the case of the world production of oil and gas? In my opinion, yes. There are some similarities; both fossil fuels and caviar are non-replaceable resources; and in both cases prices went rapidly up at and after the peak. So, if Caspian sturgeon showed such a clear Seneca cliff, oil and gas could do the same. But let me go into some details.

In the first version of my Seneca model, the fast decline of production was interpreted in terms of growing pollution that places an extra burden on the productive system and reduces the amount of resources available for the development of new resources. However, I found that the Seneca behavior is rather robust in these systems and it appears every time people try to "stretch out" a system to force it to produce more and faster than it would naturally do.

So, in the case of the Caspian sturgeon, above, growing pollution is unlikely to be the cause of the rapid collapse of production (even though it may have contributed to the problem). Rather, the main factor in the collapse is likely to have been the effect of the growing prices of a rare and non replaceable resource (caviar). High prices enticed producers to invest more and more resources in raking out of the sea as much fish as possible. It worked, for a while, but, in the end, you can't fish sturgeon which isn't there. It ended up in disaster: a classic case of a Seneca Cliff.

Can this phenomenon be modeled? Yes. Below, I describe the model for this case in some detail. The essence of the idea is that producers need to reinvest a fraction of their profits in developing new resources in order to keep producing. However, the yield of the new investments declines as time goes by because the most profitable resources (e.g. oil fields) are exploited first. As a result, less and less capital is available for new investments. Eventually production reaches a maximum, then it declines. If we assume that companies re-invest a constant fraction of their profits in new resources, the model leads to the symmetric bell shaped curve known as the "Hubbert Curve."

However, as I describe in detail below, decline can be postponed if high prices provide extra capital for new productive developments. Unfortunately, growth is obtained at the cost of a fast burning out of capital resources. The final result is not any more the symmetric Hubbert curve, but a classic Seneca curve: decline is more rapid than growth.

Is this what we are facing for fossil fuels? Of course, we are only dealing with qualitative models, but, on the other hand, qualitative models are often robust and give us an idea of what to expect, even though they can't tell us much in terms of predicting events on a precise time scale. The ongoing collapse of oil prices may be a symptom that we are running out of the capital resources necessary to keep developing new fields. So, what we can say is that there are some good chances of rough times ahead - actually very rough. The Seneca cliff may well be part of our near term future.

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The Seneca curve as the result of increasing fractions of profits allocated to the production of a non renewable resource

by Ugo Bardi - 07 Dec 2014

Note: this is not a formal scientific paper; it is more a rough "back of the envelope" calculation designed to show how increasing capex fractions can affect the production rate of a non renewable resource. If someone could give me a hand to make a more refined and publishable study, I would be happy to collaborate!

The basics of a system dynamics model describing the exploitation of a non renewable resource in a free market are described in detail in a 2009 paper by Bardi and Lavacchi. According to the model developed in that paper, it is assumed that the non renewable resource (R) exists in the form of an initial stock of fixed extent. The resource stock is gradually transformed into a stock of capital (C) which in turn gradually declines. The behavior of the two stocks as a function of time is described by two coupled differential equations.R' = - k1*C*RC' = k2*C*R - k3*C,whereR' and C' indicate the flow of the stocks as a function of time (R' is what we call "production"), while the "ks" are constants. This is a "bare bones" model which nevertheless can reproduce the "bell shaped" Hubbert curve and fit some historical cases. Adding a third stock (pollution) to the system, generates the "Seneca Curve", that is a skewed forward production curve, with decline faster than growth.

The two stock system (i.e. without taking pollution into account) can also produce a Seneca curve if the equations above are slightly modified. In particular, we can write: R' = - k1*k3*C*RC' = ko*k2*C*R - (k3+k4)*C.Here, "k3" explicitly indicates the fraction of capital reinvested in production, while k4 which is proportional to capital depreciation (or any other non productive use). Then, we assume that production is proportional to the amount of capital invested, that is to k3*C. Note how the ratio of R' to the flow of capital into resource creation describes the net energy production (EROI), which turns out to be equal to k1*R. Note also that "ko" is a factor that defines the efficiency of the transformation of resources into capital; it can be seen as related to technological efficiency. These points will not be examined in detail here.

Here is the model as implemented using the Vensim (TM) software for system dynamics. The "ks" have been given explicit names. I am also using the convention of "mind sized models" with higher free energy stocks appearing above lower free energy stocks

If the k's are kept constant over the
production cycle, the shape of the curves generated by this model is
exactly the same as with the simplified version, that is a symmetric,
bell shaped production curve. Here are the results of a typical run:

Things change if we allow "k3" to vary over the simulation cycle. The characteristic that makes "k3" (productive investment fraction) somewhat different than the other parameters of the model, is that it is wholly dependent on human choice. That is, while the other ks are constrained by physical and technological factors, the fraction of the available capital re-invested into production can be chosen almost at will (of course, there remains the limit of the total amount of available capital!).

Higher prices will lead to higher profits for producers and to the tendency to increase the fraction reinvested in new developments. It is also known that in the region near the production peak prices tend to be higher - as in the historical cases of whale oil and caviar and whale oil. In the case of caviar, the price rise was nearly exponential, in the case of whale oil, more like a logistic curve. Assuming that the fraction of reinvested capital varies in proportion to prices, some modeling may be attempted. Let me show here the results obtained for an exponential increase of the fraction of reinvested Capex.

I have also tried other functions for the rising trend of k3. The results are qualitatively the same for a linear increase and for a logistic one: the Seneca behavior appears to be robust, as long as we assume a significant increase of the fraction of the reinvested capex.

Let me stress once more that these are not supposed to be complete results. These are just tests performed with arbitrary assumptions for the constants. Nevertheless, these calculations show that the Seneca cliff is a general behavior that occurs when producers stretch out their system allocating increasing fractions of capital to production.

Hello! This is Ugo Bardi - I tend to overextend myself on the Web by writing a lot of stuff. Presently, my blog in English is titled "Cassandra's Legacy". In English, have another blog a little more esoteric, titled Chimeras. The first is dedicated to sustainability, the second to mythology, history, and art.

I can not guarantee continuity in my effort, so do not see a good idea to create a blog. On the other hand, I ´m guided by the desire to learn and to cooperate in the dissemination of knowledge about problems that afflict our world. And. i think, the best way is to support authors of prestige.

Usually I upload translations and I write posts in the Crash Oil forum. I especially like translate Posts by John Michael Greer.

Yes, but it is too bad. Placed in the comments, the translations won't have any visibility. Why should people look for translations in spanish to be found in a blog in English? You should place them in a repository, somewhere. It is what we do with the italian version of this blog: we place translations in a site of their own. We could easily make a version in Spanish. Would you be interested in putting your translations in there?

Estimated prof. Bardi, told him that are translated into Spanish some of his articles and discuss in a forum that is born in the shadow of Dr. Antonio Turiel blog.

If you are interested in seeing the comments generated, the link to one of your items is as follows: http://foro-crashoil.2321837.n4.nabble.com/Post-El-colapso-de-los-precios-del-petroleo-lecciones-de-la-historia-Ugo-Bardi-td13255.html

And for now, the forum administrator, is bringing translations of several authors in this thread: http://foro-crashoil.2321837.n4.nabble.com/Traducciones-td9121.html

Kopits presented some interesting data about capex values and oil production for the listed oil majors (pages 40-42) - http://energypolicy.columbia.edu/sites/default/files/energy/Kopits%20-%20Oil%20and%20Economic%20Growth%20%28SIPA%2C%202014%29%20-%20Presentation%20Version%5B1%5D.pdfThat might be useful for the model, but not quite enough to quantify k3...if that is necessary after all.

Ugo What do you think of these people and their model of depletion? Are they saying the same thing as you, in their case using perhaps the same kind of data as Kopits?Quote: "Optimistic estimates place the world's total petroleum reserve at 4,300 billion barrels. Of that quantity the ETP model predicts that it will be possible to extract 1,760.5 billion barrels. This constitutes 40.9% of the total reserve."

Yes, it seems that data availability is a problem for capex data of oil industry. I thought that it might be possible to compile correct values from annual reports for shareholders of respective companies (tedious task, I know), but even BP has the last downloadable report only from the year 2005. I would like to help you with the paper, but it seems that it will be a problem to find any suitable data, even for other nonrenewables.

Regarding the oil shale plays, it would seem the capex is driven by external finance rather than reinvestment of profits. I guess this also extends the peak beyond what would be capable using only reinvestment of profits.

I guess the system really is on its last legs when oil is produced non-profitably to keep the system running simply via central banks magically printing money by fiat. Obviously such slight of hand is not sustainable.

This might explain why, recently, oil prices have fallen even though production costs are high. I was going to ask Prof. Bardi if he can explain the recent price declines so near the presumed Seneca Peak. Looks like it may be from something external to the simple models he presented.

Not to put words in Prof. Bardi's mouth, but the models presented here are doubtless intended to be illustrative, not definitive. In any case, of course, "definitive" modeling is only possible after (usually long after) the modeled event(s) have run to completion and all significant factors have been (retrospectively) identified. This is the core difficulty with, for example, the global climate-change models; unforeseen-but-necessary consequences, both as to type and rate of event, keep arising. Thus the ever-moving target of "probable consequence and schedule."

"Often, people appear to be perfectly able to understand what the problem is, but, just as often, they tend to act on it in the wrong way. "

Whenever I complain to my grandmother about something in society that doesn't make sense, she tells me, "Everything makes sense to the people doing it, you just have to ask who and when does it help?"

From that perspective, I have come to accept that market failures on finite resources are what us programmers call a feature, not a bug. In the sturgeon example (and bluefin tuna is another good one) the collective industry gets richer and richer as the price rises, since profits rise faster than expenses, but even on the down slope it causes superior outcomes for some players. At first, these are the legacy players that happen to be able to hold out the longest and find a high price, lower competition environment; but eventually a lot of resources are spent even when total output is low because it becomes a lottery.

If the goal of producers was to contribute to society then you are right they are doing the wrong thing, but if it is the hope of getting rich then they are doing the absolutely correct thing. After all, the producers are able to get external financing and can restructure debt when things go wrong, so it is a heads we win, tails you lose situation with their investors.

Traditional fishing villages in Japan rarely catch bluefin these days, but any ship that does catch a few is a ticket to retirement, so a myriad of boats still set out, backed by small investor pools playing a physical equivalent of the lotto.

Random positive reinforcement is *the* strongest operant conditioner. The only factor that seems to break the cycle is complete and sustained demand destruction. As long as demand remains, even if it is just among the luxury class, these dynamics seem to hold.

This seems to make the Seneca Cliff not only plausible, but inevitable.

Mikkel's astute comments (for which thanks!) resonate perfectly with Garrett Hardin's observations on the "tragedy of the commons" so many years ago. Hence the necessity and inevitability of "demand destruction" aka collapse/depopulation so eloquently posited by the "doom-sayers."

The only way forward/out of this morass, so far as I can see, is a truly massive (and highly improbable) change/elevation of collective human consciousness. Ironically, such an event seems most likely as a late (likely too late) consequence of that "demand-destruction."

Who

Ugo Bardi is a member of the Club of Rome and the author of "Extracted: how the quest for mineral resources is plundering the Planet" (Chelsea Green 2014). His most recent book is "The Seneca Effect" (Springer 2017)

Listen! for no more the presage of my soul, Bride-like, shall peer from its secluding veil; But as the morning wind blows clear the east,More bright shall blow the wind of prophecy,And I will speak, but in dark speech no more.(Aeschylus, Agamemnon)

Ugo Bardi's blog

This blog deals with the decline of the availability of natural resources, climate change, ecosystem disruption and why all that is happening. The future may not look bright, but it is still possible to face it if we don't discount the alerts of the modern Cassandras.Above: Cassandra by Evelyn De Morgan, 1898

Chimeras: another blog by UB

Another blog by Ugo Bardi; it is dedicated to art, myths, literature, and history with a special attention to ancient monsters and deities.

The Seneca Effect

The Seneca Effect: is this what our future looks like?

Extracted

A report to the Club of Rome published by Chelsea Green. (click on image for a link)

Rules of the blog

I try to publish at least a post every week, typically on Mondays, but additional posts often appear on different days. Comments are moderated. You may reproduce my posts as you like, citing the source is appreciated! (not necessarily valid for posts written by authors other than UB)

About the author

Ugo Bardi teaches physical chemistry at the University of Florence, in Italy. He is interested in resource depletion, system dynamics modeling, climate science and renewable energy. Contact: ugo.bardi(whirlything)unifi.it